package dynamicprogramming;

/**
 * @Author: 海琳琦
 * @Date: 2022/3/2 16:54
 * https://leetcode-cn.com/problems/unique-paths/
 */
public class UniquePaths {

    /**
     * dp[i][j]：代表机器人达到i,j位置经过不同路径的个数
     * 递推公式：dp[i][j] = dp[i-1][j] + dp[i][j-1]
     * 初始化：dp[0][j] = 1; dp[i][0] = 1;
     * @param m
     * @param n
     * @return
     */
    public int uniquePaths(int m, int n) {
        int[][] dp = new int[m][n];
        //初始化
        for (int j = 0; j < n; j++) {
            dp[0][j] = 1;
        }
        for (int i = 0; i < m; i++) {
            dp[i][0] = 1;
        }
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
            }
        }
        return dp[m - 1][n - 1];
    }

    public static void main(String[] args) {

    }
}
